Together Again for Geodesy

Very Long Baseline Interferometry (VLBI) transmitters on satellites are considered for future satellites of Global Navigation Satellite Systems (GNSS) as well as for the upcoming Genesis mission of the European Space Agency (ESA). In both concepts, VLBI observations to VLBI transmitters on the satellites can contribute to orbit determination, with the geometry of observations to Genesis advantageous compared to GNSS. With Galileo as one of the GNSS, we emphasise the importance of VLBI observations for the estimation of the right ascension of the ascending node Ω $$\Omega $$ , which cannot be determined from GNSS alone. We find that Ω $$\Omega $$ can be estimated with accuracies better than 50 μ $$\mu $$ as from 24 hour sessions with alternate observations to quasars and the Galileo satellite of interest. Station coordinates, on the other hand, can be determined from observations to three Galileo satellites with an accuracy at the centimetre-level or better from 24 hour sessions, again with alternate observations to the satellites and quasars for a better estimation of tropospheric parameters. Station coordinate results with VLBI observations to VLBI transmitters on satellites form the basis for frame tie and local tie determination. The transfer of space ties to local ties on the ground is of particular relevance for Genesis.

Large constellations of low Earth orbit (LEO) satellites equipped with Global Navigation Satellite System (GNSS) receivers open the possibility of forming a dense and homogeneous GNSS network in space, covering the entire Earth. Based on simulations, this study investigates how geodetic Earth observation could benefit from this development. In the first part, we compare the effects of different processing strategies, parameterizations and simulated errors. The results show that for a large number and a uniform distribution of satellites in a constellation, GNSS network (double-difference) processing can improve LEO orbit determination compared to a single-satellite (zero-difference) processing, provided that the integer ambiguities have been correctly resolved. In the second part of this study, we demonstrate that in a LEO constellation with 36 uniformly distributed satellites, an accuracy of about 1 cm (3D RMS) for the a-priori LEO orbits and about 3 cm for the GNSS orbits is required to achieve the sufficient ambiguity-fixing rate necessary to take full advantage of the double-difference processing.

With the GENESIS proposal accepted, this study reevaluates the implementability of incorporating VLBI observations of satellites into geodetic VLBI experiments. Observations of NavIC system satellites were carried out using the 12-m AuScope radio telescopes in Hobart and Katherine. The primary focus is on scrutinizing the necessary efforts within the VLBI community aimed at effectively supporting the GENESIS satellite mission. Our investigation identifies limitations in the existing processing pipelines, particularly in the generation of station-specific procedure and local control files, as well as in satellite tracking support within the antenna control units, resulting in step-wise tracking rather than continuous tracking. Additionally, we have conducted an analysis to ascertain the effective visibility of the GENESIS satellite within both current and future VLBI networks. Our findings align with the envisioned visibility criteria of GENESIS when more VGOS-type stations are integrated into the current network. In this case, the satellite becomes visible from at least two stations with long baselines for approximately 75.6% of the time during experiments and 21.5% of the time in a year.

A geodetic datum describes the origin, orientation and scale of a station network, typically with respect to a reference frame. In the analysis process of Very Long Baseline Interferometry (VLBI) observations, the introduction of a geodetic datum is inevitable for the determination of precise reference frames and Earth orientation parameters (EOP). In general, several methods of datum definition exist within the VLBI community, including Helmert rendering and the no-net-translation/no-net-rotation (NNT/NNR) approach. While the first introduces conditions with quasi-infinite weight, the NNT/NNR method can be controlled by the selection of formal errors. Evaluations of the CONT17 legacy-1 campaign and a longer time series of IVS 24-hour sessions show that the variance information (formal errors) of the estimated terrestrial reference frames based on the different methods can differ in the mm to almost cm range. Neglecting this issue could lead to potential issues when combining or comparing solutions from different analysis centers.

Solar Radiation Pressure (SRP) is the largest non-conservative force acting on Global Navigation Satellite Systems (GNSS) satellites. Modeling this force is still one of the challenging tasks in precise orbit determination (POD) of GNSS satellites and therefore also for subsequent applications as geodetic reference frame determination. Commonly used methods for SRP modeling are empirical or analytical ones, as well as combinations of the two. These points give rise to the motivation whether and how alternative observation techniques can improve future GNSS and support them in aspects of POD, reference frame determination and other subsequent applications. For this purpose, we analyze the potential of accelerometers onboard of each Galileo satellite by using simulations for different accelerometer specifications and evaluate the effect on position and clock estimates of the satellite vehicle, as well as the effect on derived Terrestrial Reference Frames (TRF). We thereby see, by assuming accelerometer sensitivities which are already available, the possibility to decorrelate the clock estimates from radial orbit position determinations. The advantages for GNSS based positioning are limited, since radial orbit errors and clock errors almost perfectly compensate. Promising potential for improvements for derived TRF and geocenter determination can be seen, which would bring us one step closer to achieving the accuracy requirements of a global TRF, defined by the Global Geodetic Observing System (GGOS).

Following extensive evaluations, the latest realization of the International Terrestrial Reference System (ITRS), the International Terrestrial Reference Frame (ITRF) 2020 (ITRF2020), was published at the end of last year. For operational application, certain extensions of an ITRF are generated by the services of the different space geodetic techniques. The extension of the ITRF2020 for the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) technique, is the recently released DPOD2020, which is generated by the International DORIS Service (IDS). In this study we exhibit the differences that we see in the application of the DPOD2020. For this purpose, we use altimetry satellites equipped with a DORIS receiver in a setup using the latest DPOD2014 and DPOD2020. Initially we performed Precise Orbit Determination (POD) and evaluate the differences we see internally, in terms of the orbital fit, as well as changes in the derived orbit. Subsequently, weekly local terrestrial reference frames (TRFs) are computed for each single satellite as well as a combined solution to evaluate the impact on derived station coordinates and Earth Rotation Parameters (ERPs). The following generated TRF solutions are evaluated with respect to the reference frame defining parameters, i.e. origin, scale, and orientation, in comparison to the a priori TRF and as differences between ITRF2014 and ITRF2020 solutions. The processed orbits show comparable results w.r.t. orbital fits and orbit comparisons between both solutions. The local TRF’s show also overall good agreement between the ITRF2020 and ITRF2014 solutions with no systematic bias.

Since 1991, the International Terrestrial Reference Frame (ITRF) includes the global time evolution of station positions (velocities) in addition to the three-dimensional Cartesian station positions at a fixed reference epoch. The orientation of the velocities refers to a kinematic model of rigid tectonic plates derived from geophysical observations over millions of years. For consistency with other geodetic parameters (e.g., Earth orientation), the models must be aligned to actual no-net-rotation of the whole Earth surface. Because of deviations of present-day velocities and neglect of non-rigid surface deformations, e.g., in seismic zones, the geophysical models are not valid for today. This paper describes a further developed method of estimating a non-rotating terrestrial reference frame from space geodetic observations. Different to previous estimations of geodetic no-net-rotation models, regional inter-plate and intra-plate crustal deformations are included, and instead of using the irregularly distributed observed station velocities, an evenly distributed grid throughout the Earth is interpolated by least squares collocation. Due to significant changes of the station velocities from one ITRF to another, NNR models must be computed for each ITRF. Here it is done for the ITRF2020.

IAG Commission 1 Working Group 1.3.1 in association with the Open Geospatial Consortium (OGC) have developed a functional model for crustal deformation (FMCD) and an associated Geodetic Grid Exchange Format (GGXF) for quantifying and disseminating deformation information for use in time-dependent reference frame transformations.The FMCD provides a framework within which producers and users of deformation models can describe crustal displacement and velocity data using robust grid formats such as GGXF. Using the FMCD and GGXF combined, positional displacements can be readily applied in point motion coordinate operations and non-conformal time-dependent transformations. This approach is essential in deforming zones where conformal time-dependent transformation approaches do not adequately handle crustal deformation.This paper describes application of the FMCD in typical cases including: (1) transformation of GNSS PPP positions (e.g. in an IGS20 frame) to a national geodetic datum in a deforming zone and (2) transformation between reference frames across earthquake events that resulted in significant coseismic and postseismic crustal displacement. The FMCD and associated GGXF provide a framework for developers of geodetic software such as those used in GIS, GNSS processing and positioning to better handle complex deformation.

A global combined GNSS velocity field with almost 13,400 sites has been derived by the International Association of Geodesy’s Joint Working Group 3.2. The combined field is aligned to the ITRF2020 and gathers global and regional velocity fields computed by nineteen groups using different approaches. In addition to the combined velocities and their uncertainties, the combination also provides the alignment of each velocity field to the ITRF2020, the scaling of their velocity uncertainty and the estimated repeatability of the velocity estimates across the different groups at almost 3,000 sites. The median repeatability is at the level of 0.17 and 0.27 mm/yr for the horizontal and vertical velocities. Up to 11 % of the sites show poor velocity repeatability exceeding 3 times the median values.

The Earth’s crust experiences deformation caused by a range of geophysical phenomena, including the motion of tectonic plates and the redistribution of surface fluids like the atmosphere, oceans, and continental water. These natural processes result in substantial changes in the Earth’s crust load, leading to the displacement of geodetic sites and alterations in station coordinates over time scales that can vary from yearly to sub-diurnal periods. Geophysical models are employed in Very Long Baseline Interferometry (VLBI) analysis to consider loading effects resulting from the global movement of the geophysical fluids to accurately estimate parameters of interest. Given VLBI’s significance as a key technique for terrestrial reference frame determination, the accuracy of geophysical models becomes paramount. This study focuses on comparing elastic surface loading products, specifically on the corresponding changes in station coordinates. Non-tidal surface loading (NTSL) data is obtained from different loading services, such as VieAPL, EOST, IMLS, and ESMGFZ. Notably, VieAPL exclusively provides non-tidal atmospheric loading (NTAL), while EOST, IMLS, and ESMGFZ provide all three NTSL components—NTAL, non-tidal oceanic loading, and hydrological loading. The analysis of 20 years data of NTSL (from 2001 to 2020), extracted from these services demonstrates consistency among them, except for the hydrological loading component of ESMGFZ. The implementation of NTSL models in VLBI analysis has revealed that baseline length repeatability shows improvements or remains stable in 90.25% of the baselines for IMLS, 89.02% for EOST, and 86.18% for ESMGFZ. Additionally, the application of NTSL models leads to an improvement in the standard deviation of station height by 65% in both EOST and IMLS, and by 61.25% in the case of ESMGFZ. We also investigate the variance reduction coefficients, demonstrating the distinctions in loading corrections offered by various services.

This study investigates the effects of non-tidal atmospheric loading on GNSS time series for a network covering the Nordic countries, with a specific focus on Finland. We processed a 5-month dataset from the year 2015 using GAMIT/GLOBK software, implementing two distinct non-tidal atmospheric loading grid models, namely ‘atmfilt’ and ‘atmdisp’. Our results reveal that both grid models yield similar improvements in the variability of GNSS coordinate time series, albeit with a slightly better performance for ‘atmdisp’ grid. Our results show that implementing these built-in models in the time series analysis yields up to a 14% improvement (reduction in scatter) in the vertical component for 75% of the selected stations. However, the enhancement diminishes for the horizontal components (increase in scatter), exacerbating the eastern component of time series. The corrections lead to a 10% improvement of the North component. We also examined the effectiveness of the loading corrections by comparing our processing-level corrected time series to the daily averaged time series improved by the loading model provided by EOST loading service as a post-processing approach. Given the relatively short 5-month duration of the time series, drawing definitive conclusions when comparing models is challenging. However, it is evident that the GNSS time series exhibits distinct variations related to atmospheric loading in their vertical positions across the various models that were examined.

The PSInSAR (Persistent Scatterer Interferometric Synthetic Aperture Radar) technique allows determining deformation maps over large areas. In this paper, we investigate the applicability of PSInSAR analyses for ITRF co-location sites characterized by spatial extents varying between 20 m and 3 km. Although PSInSAR shows some limitations such as spatial resolution and sparse Persistent Scatterer distribution, this technology can be used to determine relative motion between geodetic instrumentation at sufficient spatial detail, specifically for large sites. The spatial resolution varies from 3 × 22 m [rg × az] from typical Sentinel 1A/1B products (IW mode) to 0.6 × 0.25 m [rg × az] for staring spotlight mode of TerraSAR-X/Tandem-X. As an illustration, C-band PSInSAR results derived by the European Ground Motion Service (EGMS) from Sentinel 1A/1B images have been investigated for the five largest ITRF co-location sites in Europe. Maximum relative velocity differences have been found to be smaller than 2.0 mm/yr. Moreover, as high-resolution X-band SAR images show great potential for mapping deformations at high resolution, an inventory of already available TerraSAR-X/Tandem-X images at ITRF co-location sites has been established. Based on this, five candidate sites are proposed for further PSInSAR analyses using X-band data.

The geodetic method of positional data processing is usually not one of position estimation only, nor one of model testing only, but usually one in which estimation and testing are combined. The Detection, Identification and Adaptation (DIA)-estimator captures the statistical intricacies of this combination, providing a unifying framework for rigorous analyses of positional integrity and quality control procedures. However, to be able to establish fit-for-purpose quality control, not only solutions for the forward problem (quality of control) need to be available, but also for the inverse problem (control of quality). With the DIA-estimator and its multi-modal probability density function (PDF), we have solutions available for the forward problem, but not yet for the inverse problem. That is, no objective methods and strategies are currently available that allow one to design DIA-estimators specifically for given fit-for-purpose quality criteria. In this invited contribution we present and illustrate some of the underlying design and computational challenges that are brought forward by the complexities of the inverse problem. This relates, amongst others, to the DIA-variables, such as the chosen partitioning of the misclosure space, and to the ‘winner-takes-all’ structure of the DIA-class of estimators currently employed. To appreciate the fundamental differences with the traditional estimation-only approaches, we also show how the position probability distribution, and therefore the quality of positioning, is affected and driven by the combination of estimation and testing. For an underpinning of the design and computational challenges various numerical and graphical examples are presented.

The adjustment of parameters from different observations describing the state and change of system Earth has been conducted at the Helmholtz Centre Potsdam—GFZ German Research Centre for Geosciences via satellite observations for many decades. Satellite Laser Ranging (SLR) is used to establish ground station coordinates and their drifts as well as Earth Rotation Parameters (ERPs). Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), Global Navigation Satellite System (GNSS), SLR and Very Long Baseline Interferometry (VLBI) observations are combined to contribute to the development of an International Terrestrial Reference Frame (ITRF) with the highest precision possible. The Earth’s gravity field and its temporal variations are adjusted analyzing orbit perturbations of Low Earth Orbiting (LEO) satellites, where the corresponding trajectories are obtained from Global Positioning System (GPS), on-board accelerometers (ACC) or gradiometers, star tracker (STR) and inter-satellite ranging observations. Apart from real data analysis, numerous simulation studies are conducted, e.g. to investigate the performance of Next Generation Gravity Missions or possible improvements of terrestrial reference frames by space-tie satellites. Also, we contribute to testing the theory of general relativity by analysing observations of the Laser Geodynamic Satellites (LAGEOS). All that would not be possible without a universal software tool that is central to all these activities. In this paper we give a short overview of our program package Earth Parameter and Orbit System (EPOS) with its core module for precise orbit computation (OC) EPOS-OC. We briefly describe its main features and give examples on Precise Orbit Determination (POD) of Earth satellites, describe how the program is used for determination of ERPs, station coordinates, reference frames and the adjustment of Earth’s gravity field using real-world data and within simulation studies. We finally show that EPOS-OC is also a useful tool to test some predictions of the theory of General Relativity.

Free Core Nutation (FCN) arises from complex geophysical processes causing misalignment between the mantle and the liquid core, and exhibits a retrograde motion with a period of about 431 days as observed by Very Long Baseline Interferometry (VLBI) as part of the celestial pole offsets (CPO). This study assesses the influence of using an empirical model of FCN on estimating Earth Rotation Parameters (ERP) from different types of VLBI sessions, i.e., 24-hour S/X sessions (2001–2022), 24-hour VGOS sessions (2019–2022), and Intensive sessions (2001–2022). To evaluate the impact, a priori values of CPO from the IERS Bulletin A series and the FCN model by Belda et al. (2016) are used, and the estimated polar motion and UT1-UTC values are compared against the IERS 20 C04 EOP solution. The results indicate that the sole application of the empirical FCN model does not degrade the WRMS values but introduces time-dependent systematic differences in ERP. The comparison of S/X and VGOS sessions indicates that ERP estimated using the Belda model in VGOS sessions demonstrate slightly lower WRMS values.

The Earth Orientation Parameters (EOPs) describe the rotation between the Terrestrial Reference Frame and the Celestial Reference Frame and represent an essential component of the Global Geodetic Reference Frame. This study presents the current activities of BKG in the area of combined processing of GNSS and VLBI data in one common adjustment with the main objective to generate a consistent combined EOP time series. In earlier studies, we have investigated different combination approaches using VLBI and GNSS data. We generate EOP series with latencies of about one to 14 days, depending on the input data we used. In this way, a significant improvement in accuracy compared to the individual technique-specific solutions was achieved, especially for the highly variable component dUT1. The combination process starts at the level of normal equations using an EOP parameterization with piece-wise linear offsets and a temporal resolution of one day. Our main objective is to generate a continuous, daily and regular EOP product with the shortest possible latency. The requirement for achieving these characteristics is the daily and rapid availability of the input data. In particular, the VLBI Intensive (INT) sessions play an important role in the precise and rapid estimation of the UT1-UTC component. Since 2020, an increasing number of VLBI Global Observing System (VGOS) INT campaigns has been conducted in addition to the legacy S/X INT sessions. The VGOS network is under continuous extension and the accuracy and latency of the VGOS INT sessions are at least at the level of the legacy S/X sessions. Therefore, an inclusion of the VGOS INT data is beneficial for rapid EOP estimation. The integration of the VGOS data into the combination process results in a constant slight decrease of the Weighted Root Mean Square (WRMS) level of the UT1-UTC residuals in comparison to the external EOP series. The growing number of available INT sessions with independent networks, up to four per day, increases the continuity and reliability of the combined EOP solution.

Forecasts of Earth’s Effective Angular Momentum functions (EAM) are used for different applications, including prediction of Earth Orientation Parameters (EOPs). Since May 2021, the Chair of Space Geodesy at ETH Zurich has been operationally providing accurate EAM forecasts. These forecasts cover the domain of atmosphere, ocean, hydrology, and sea level. They are based on the EAM forecasts by GFZ Potsdam but are corrected and extended to cover a forecasting horizon of two weeks using machine learning techniques. Here, we present a summary of the methodology and the results achieved during the past two years. We demonstrate the enhanced accuracy of our improved EAM functions of up to 50%. Furthermore, we demonstrate the impact on the potential application of utilizing EAM forecasts in the form of ultra-short-term prediction of length of day, where an improved accuracy of up to 19% has been achieved. The improved EAM forecasting product is updated daily and available at https://gpc.ethz.ch/EAM/ .

We use the GINS/DYNAMO software to produce hourly time series of Earth Rotation Parameters (ERP) from 2017 to 2022. Data from the American constellation GPS and the European constellation Galileo are used. Single solutions and combined solutions are produced and analyzed. The best spectral coherence between constellations lies in the retrograde semi-diurnal band. We also perform least-squares adjustments for main tidal frequencies and compare with those of previous works. A sliding window analysis reveals time variation of amplitudes of several main tides when adjusting on a selected set of frequencies.

Real-time Earth Orientation Parameters (EOP) are crucial in various space geodetic applications, from satellite navigation to weather forecasting. This study introduces a refined prediction package leveraging diverse EOP series from the Federal Agency of Cartography and Geodesy (BKG), including rapid and final series, Satellite Laser Ranging (SLR) series, and International Earth Rotation and Reference Systems Service (IERS) C04. Our approach yields substantial improvements in EOP prediction accuracy. Results highlight superior performance in critical parameters such as Polar Motion, (UT1-UTC) dUT1, and Length of Day (LOD) predictions. Notably, our predictions surpass benchmarks from the Second EOP Prediction Comparison Campaign (2nd EOP-PCC)” organized by International Association of Geodesy (IAG) and IERS, showcasing the effectiveness of our methodology. Additionally, BKG’s Rapid EOP stands out with remarkable accuracy, featuring a shorter latency of 1 to 2 days. This study contributes to our understanding of Earth’s rotational dynamics. It provides practical advancements in real-time EOP predictions, demonstrating the potential impact on a wide range of scientific and operational applications.

When estimating time-variable gravity field models from GRACE Follow-On data, a set of a priori given background force models is introduced in the processing to enable the computation of monthly snapshots of spherical harmonic coefficients representing the state of the Earth’s gravity field. The to-be-estimated spherical harmonic series has to be truncated at a certain point, for GRACE Follow-On commonly at degree and order 96, and one of the background models is usually a model for the gravity field itself, which is used to reduce higher frequency static gravity field signal to avoid aliasing (contained in degrees above 96).In this study we take a look on the influence of different strategies to treat the high degree gravity field signal in monthly gravity field solutions from GRACE Follow-On data. We estimate temporal gravity fields with fixed high degrees of different a priori background gravity field models, and opposed to this, we also co-estimate static spherical harmonic coefficients from degree 97 up to degree and order 160 from 51 months of GRACE Follow-On data along with the monthly snapshots to enable a consistent handling of correlations between time-variable and static gravity field coefficients. The observation noise modelling of the data is handled by an empirical covariance estimation for the noise based on post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations. Since the post-fit residuals, amongst other things, depend on the choice of the background force models they are a potential carrier of a priori information into the final solution.The results show that a formal correlation between the time-variable and static gravity field coefficients is almost non-existent, and also the empirical covariance model has only minor impacts on this correlation. Only a poor choice of the background gravity field requires a prior or co-estimation of the static gravity field.

Accelerometers (ACCs) in low-low satellite-to-satellite gravimetry missions measure the non-gravitational forces acting on the spacecraft that have to be taken into account to derive the gravitational contribution in the distance variations. Multiple ACCs form a so-called gradiometer that measure the gravity gradient. In satellite gravimetry up to now, only electrostatic ACCs were used, which are one of the main instrumental limitations due to their error contribution at low frequencies, known as drift.In this paper, we compare the performance of electrostatic ACCs at low Earth orbits with other sensors, i.e. so-called Optical ACCs based on flight heritage of the LISA-Pathfinder mission, and theoretical ACC concepts, for example Cold Atom Interferometer (CAI) ACCs and hybridized sensors (combination of electrostatic and CAI ACCs) in terms of static gravity field recovery. Under our assumptions, in particular that high-frequency variations of the gravity field can be perfectly modeled and removed during gravity field recovery, the results may be limited in the future by the performance of the LRI.We also discuss the outcomes from the various novel satellite formation flights (SFF) that utilize two orbits that differ either by right ascension of the ascending node (RAAN) or by inclination in order to acquire ranging information in the cross-track direction. The closed-loop simulations from both scenarios showed significantly lower order of magnitude of the residuals w.r.t. reference gravity field than from the anticipated future performance of the solely in-line GRACE-like satellite pair. Moreover, these triple satellite formations provide better multi-directionality of the retrieved data, avoiding the North-South striping behavior. However, it is worth noting that in such formations significant modifications are needed in the satellite bus, ACC test mass readout, LRI beam steering mechanism, etc. in order to be capable of measuring the cross-track range changes at higher range rates w.r.t. in-line GRACE-like configuration. In addition, a substantial reduction of costs in building and launching only three satellites rather than four as in double-pair constellations could be an advantage for such formations.

GRACE and GRACE Follow-On inter-satellite ranges and thereof derived range-rates are the main observables for the determination of monthly snapshots of the Earth’s gravity field. These observations are sensitive to the mass distribution on the Earth, and as a consequence, the relative motion between the missions’ satellite pairs. The range-rate observations exhibit a number of difficult-to-identify error sources and efficient screening of the data is not trivial. Therefore, we apply machine learning based outlier detection methods such as isolation forests, to flag outliers in an unsupervised fully automated way. We apply the technique to post-fit residuals of monthly, joint orbit and gravity field determination processes, combined with the geographical position of each observation. The flagged outliers are investigated for local geographical correlations to distinguish between unfitted signal from gravitational sources and artefacts caused by the satellites’ instrumentation. For that purpose we train a mutual information neural network, learning the mutual information between the post-fit residuals and the geographical location. Outliers flagged as artefacts are removed from the original inter-satellite range-rate data and the orbit and gravity field determination process is repeated to investigate for improvements. The automated outlier detection with isolation forests performs similar, at times slightly better, to empirical screenings by visual inspection of post-fit residuals. In addition, the mutual information can be taken as a valuable source to detect geophysical signal remaining in the post-fit residuals.

Satellite Laser Ranging (SLR) is essential for the geodetic parameter determination, e.g., geocenter and station coordinates, and, therefore, for long-term stable reference frame realizations. However, the orbit modeling and the quality of the parameter estimation partially depend on the background models. This study analyses the impact of static and time-variable a priori gravity field models provided by the Center for Space Research (CSR), the International Laser Ranging Service (ILRS), and the Combination Service for Time-variable Gravity Fields (COST-G) on the SLR data processing of spherical geodetic SLR satellites (LAGEOS-1/2 and LARES) at different orbital altitudes, by comparing the estimates of Earth rotation parameters, station coordinates and observation residuals. The COST-G model is further used to examine the impact of the mean pole model and the replacement of the spherical harmonic coefficients C 21 ∕ S 21 $$C_{21}/S_{21}$$ according to convention provided by the International Earth Rotation Service (IERS).While for LAGEOS-1/2 SLR data processing the a priori gravity field model has only a minor impact, the lower flying LARES satellite is more sensitive to the Earth’s gravity field and requires a more sophisticated gravity field modeling, e.g., COST-G Fitted Signal Model (FSM). In order to achieve higher consistency and thus improved solutions, the same mean pole model should be used in the SLR data processing as for the generation of the used a priori gravity field model.This study confirms the high quality of the COST-G FSM and demonstrates its suitability for potential use in the ILRS operational SLR processing.

The gravitational potential uncertainty process arising from the stochastic consideration of generally shaped polyhedra is outlined and tested on the real shape model of asteroid Psyche. The examined method is based on the computation of partial derivatives of spherical harmonic coefficients as implied by corresponding coordinate changes of the polyhedron’s vertices, while the derived results are compared with gravity signal differences induced by the shape’s variations using the line integral analytical approach. For the numerical tests, 3 regular grids of points with dimensions 600 km2 were considered. The differences of the obtained results between the two approaches range from 85 m2/s2 to 300 m2/s2 for the gravitational potential uncertainties and from 2% to 2.4% for the normalized gravitational potential uncertainties. Additional tests were carried out on different points with increasing distance from the asteroid’s surface to correlate the computed uncertainties with the spherical harmonic coefficients’ maximum degree of expansion. As seen, inside the uncertainty region defined by the boundary of Brillouin sphere, the computed normalized gravitational potential uncertainties differ at the level of 0.04% for solutions of maximum degree of expansion {5, 10, 15, 20} while outside they gradually become identical. Therefore, the position of the computation points as well as the morphology of the examined mass distribution that defines the Brillouin sphere seem to strongly affect the derived results.

The horizontal components of the airborne gravity vector are equivalent to the deflection of the vertical at the flight level and contain signals of the slope of Earth’s gravity field. We test the contribution of such components in finding the optimum flight line spacing for geoid modelling. We use the one-step integration method and create a system of linear equations containing the three components of the airborne gravity vector as observations and solve the geodetic boundary value problem on the reference ellipsoid as an overdetermined weighted least-squares problem. We test our methodology in the Colorado region in the USA given that it is one of the most challenging areas for geoid modelling. We show that by incorporating the horizontal components at the flight level, one can increase the flight line spacing by almost 40%, thereby significantly reducing the cost of airborne surveys while maintaining the same accuracy in the estimated geoid heights as when the scalar value of gravity is used.

The Atmospheric attraction computation service (Atmacs) of BKG provides atmospheric corrections for terrestrial high-precision gravity measurements based on operational weather models of the German Weather Service (DWD). In Atmacs, Newtonian attraction and deformation contributions to atmospheric loading are computed separately. The attraction component benefits from the discrete 3D distribution of air masses around the station, while deformation effects are derived from surface atmospheric pressure changes assuming that the oceans respond to atmospheric forcing as an Inverse Barometer (IB). Several improvements in the modelling approach of Atmacs are presented. A revision of the IB hypothesis implementation revealed that the attraction component over oceans was overestimated. A modification of the IB implementation not only resolves this issue but further enhances the compatibility between the atmospheric modelling and ocean models. This allows to complement Atmacs with non-tidal ocean loading effects, here based on the Max-Plank-Institute for Meteorology Ocean Model (MPIOM). These updates allow for a consistent combination of atmospheric and ocean models and a more efficient reduction of the signal recorded by high-precision terrestrial gravimeters.

In the scope of initial studies for a post-LHC (Large Hadron Collider) particle accelerator, the design and feasibility of the Future Circular Collider (FCC) at CERN are studied. In the FCC Geodesy project, which belongs to these initial studies, a high-precision geoid model for the significantly larger FCC area will be computed. The pre-alignment of the magnets and thrusters in the tunnel requires a very accurate high-resolution local geoid model with a precision of up to 30 μ m $$\mu \mbox{m}$$ over 225 m.The data sets containing gravity and deflections of the vertical measurements are described. Then, an overview of the existing (quasi)geoid models in the area is shown and representative models are compared to a newly calculated quasigeoid model. This model is the first gravitational (quasi)geoid model that was estimated specifically for this region in a least-squares adjustment. The highest correspondence of the preliminary FCC Quasigeoid was found with CHQua04 published by Switzerland and RAF20, which is a hybrid regional quasigeoid for France. The smallest offset between two models was found between the FCC Quasigeoid and XGM2019. A comparison of the new solution with GNSS-levelling datasets showed a good agreement with a standard deviations of < 1 $$<1$$ cm in the region of interest.This publication aims to provide an overview of the objectives of the FCC Geodesy project, to show the available data sets of gravity and deflections of the vertical measurements and the results of a first comparison of existing and the newly calculated FCC (quasi)geoid with GNSS-levelling points.

To ascertain the origin of the Yangju-Circular-Structure (YCS), located north of Seoul, South Korea, extensive gravity surveys were conducted. A collaborative analysis, integrating geology, geomorphology, gravity field interpretation, and density modeling, yielded significant insights:(1) The eastern region of the YCS, adjacent to the Dongducheon fault line, has been displaced approximately 3,000 m southward. This substantial shift provides crucial evidence of significant tectonic activity affecting the area. (2) Our analyses indicate that the formation of the YCS is unlikely to be a result of differential weathering processes. (3) The YCS features three distinct concentric circular structures with varying in diameter. (4) The subsurface structure beneath the YCS appears to be symmetrical, likely resulting from concentric energy waves caused by an external impact, such as a meteorite.

The Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG) promotes the standardisation of height systems worldwide. The GGOS Focus Area Unified Height System (GGOS-FA-UHS) was established to lead and coordinate the efforts needed towards the establishment of a global standard for the precise determination of physical heights. During the 2011–2015 term, various discussions focused on the best possible definition of a global unified vertical reference system, resulting in the IAG Resolution for the Definition and Realisation of an International Height Reference System (IHRS), which was adopted at the 2015 General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Prague, Czech Republic. During the period 2015–2019, activities were undertaken to investigate the best strategy for the implementation of the IHRS; i.e., the establishment of the International Height Reference Frame (IHRF). A preliminary selection of stations for the IHRF reference network was made and different calculation methods for the determination of potential values as IHRF coordinates were evaluated. For the period 2019–2023, the objectives of the GGOS-FA-UHS focused on (i) compiling detailed standards, conventions and guidelines to support a consistent determination of the IHRF at global, regional and national levels; (ii) coordinating with regional/national experts in gravity field modelling the computation of a first IHRF solution; and (iii) designing an operational infrastructure that will ensure the long-term sustainability and reliability of the IHRS/IHRF. This infrastructure was approved by the IAG Executive Committee in December 2023 and will operate under the responsibility of the International Gravity Field Service (IGFS). With these objectives achieved, the GGOS-FA-UHS completed its goals and was closed during the IUGG 2023 General Assembly in Berlin, Germany. This paper presents a comprehensive report on the activities and achievements of the GGOS-FA-UHS.

The International Association of Geodesy (IAG) introduced the International Height Reference System (IHRS) in 2015 as an international standard for the accurate determination of physical heights worldwide. Primary vertical coordinates are geopotential numbers referenced to a conventional W0 value. The realisation of the IHRS is the International Height Reference Frame (IHRF), which corresponds to a global network of reference stations with precise reference coordinates specified in the IHRS. The spatial position of the stations, at which the geopotential numbers are calculated, is defined by their respective coordinates (X, Y, Z) in the International Terrestrial Reference Frame (ITRF). The realisation of the IHRS is thus based on the combination of a geometric component, given by the positions of the stations in the ITRF, and a physical component, given by the determination of the potential values W at these positions. Through a strong international collaboration, framed by the IAG, it has been possible in recent years to pave the scientific foundations of the IHRS, to compute a first solution of the IHRF, and to identify the key requirements for a long-term sustainability of the IHRF. Much progress has been made and continuity is needed to ensure the maintenance and availability of the IHRF in the future. Following IAG practice, the development of theory and methods for the continuous improvement of the IHRS/IHRF should be promoted by the IAG Commissions and the Inter-Commission Committee on Theory (ICCT), while the operational performance should be ensured by the IAG Services. In this paper, we highlight the organisational challenges in maintaining the IHRS/IHRF, discuss how the existing gravity field related IAG Services could contribute to the IHRS/IHRF, and identify the elements needed to establish an operational infrastructure for the IHRS/IHRF that addresses the organisational challenges. Our proposal is to establish a central coordinating body under the responsibility of the International Gravity Field Service (IGFS), composed of individual modules taking care of the main components of the IHRS/IHRF. The central management body is the IHRF Coordination Centre and its modules are the IHRF Reference Network Coordination, the IHRF Conventions’ Coordination, the IHRF Associate Analysis Centres, and the IHRF Combination Coordination. The IGFS presented this proposal to the IAG Executive Committee at its meeting on 10 December 2023 and it was unanimously approved. Thus, a new component of the IGFS dedicated to the IHRF has been created and will ensure the long-term availability and reliability of the IHRF.

One of the current goals of the International Association of Geodesy (IAG) through its Global Geodetic Observing System (GGOS) is the unification of the existing local vertical datums towards the realization of the International Height Reference System (IHRS), i.e. the International Height Reference Frame (IHRF). To achieve this goal, one possible solution is to compute the offset between the equipotential surface of the Earth’s gravity field realized by the conventional W 0 IHRF $$W_0^{\text{IHRF}}$$ value of the IHRS and the unknown geopotential value of the local vertical datum. This offset is known as vertical datum parameter. In this study, the determination of the vertical datum parameter of the Argentinean National Vertical Reference System 2016 (SRVN16) using two approaches is presented. The first approach is based on the Geodetic Boundary Value Problem (GBVP). The second approach combines geopotential numbers obtained with levelling and gravity with geopotential numbers derived from a quasigeoid model. Both methods require GNSS/Levelling data and a high-precision gravimetric quasigeoid model. The quasigeoid model was computed using the remove-compute-restore technique and applying a Fourier representation of Molodensky’s integral formula. The vertical datum parameter estimation was carried out in a flat area in the Buenos Aires province due to the availability of high-quality gravity observations and benchmarks with GNSS/Levelling-derived height anomalies, all located near the tide gauge station used to define the Argentinean vertical datum. Estimation results with the first and second approach were −0.46 ± 1.78 m 2 s −2 $${-}0.46 \pm 1.78 \text{ m}^2\text{s}^{-2}$$ and −0.46 ± 1.37 m 2 s −2 $${-}0.46 \pm 1.37\ \text{m}^2\text{s}^{-2}$$ , respectively. The vertical datum parameter can be further used to integrate SRVN16 into the IHRF.

The International Association of Geodesy (IAG) introduced and defined, in 2015, the International Height Reference System (IHRS) as the conventional reference system for the global physical height determination. Following the conventions for the realisation of the IHRS, i.e. the determination of the International Height Reference Frame (IHRF), we utilize the existing GNSS reference stations in Denmark, The Faroe Islands, and Greenland to determine a local densification of the IHRF in these regions. The physical heights of these Danish, Faroese and Greenlandic GNSS reference stations have been transformed from the local Danish, Faroese, and Greenlandic height systems, DVR90, FVR09 and GVR16, respectively, to geopotential numbers and normal heights referring to the IHRF. The offset to the IHRF is found to be −44.0 ± 1.9 cm, −59.8 ± 5.1 cm and − 54.1 ± 11.3 cm for the DVR90, FVR09 and GVR16, respectively. This transformation relies on the existing precise local (quasi-)geoid models. This contribution describes the applied procedures in the IHRF densification and discusses the quality assessment of the results.

Satellite radar altimetry has been providing sea surface heights on an almost global scale for the past 30 years. From this data, an average global mean sea level rise of 3-4 mm per year can be estimated. To determine these small changes with high accuracy, precise and stable measurements are required. Long-term data stability is particularly important for sea-level rise applications. This not only relates to the altimeter measurements themselves, but also to any geophysical correction applied to the data. Furthermore, consistency between different missions is essential to ensure a long time series that is useful for climate studies.This contribution shows how global sea level rise estimates can be affected by geophysical corrections applied to satellite altimetry data and the importance of selecting the right datasets. The focus will be on atmospheric corrections, especially on different wet troposphere path delay corrections derived by models and observations. It will be shown that these corrections can introduce systematic errors in the order of 0.5 mm/year, which is the level of uncertainty currently assumed for the altimetry-derived global mean sea level trend.

The bathymetry of coastal bay environments, such as Moreton Bay near Brisbane in eastern Australia, is constantly reworked because of changes in energy dispersal and related sediment transport pathways. Updated and accurate bathymetric models are a crucial component for scientific, environmental, and ship safety studies.NASA’s Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) is equipped with a laser detecting system (green light) that penetrates the air-water interface. Under optimal conditions, it can provide shallow water bathymetry (depths <40 m). We attempted to use ICESat-2 measurements to study bathymetry and possible bathymetry changes from repeated tracks across Moreton Bay. We found that the water turbidity in Moreton Bay varies with time. More than half of the water area is affected by suspended sediment, which makes ICESat-2 difficult to obtain bathymetric measurements. In other areas, repeated ICESat-2 tracks performed consistently on the 1-meter level. This means that ICESat-2 can be used to update existing bathymetry in the region. We also devised a method to determine bathymetry in the shallower parts of the zone affected by mud.

As part of the European Copernicus program the radar altimetry satellites Sentinel-3A and Sentinel-3B were launched in 2016, and 2018 respectively. The satellites are one of the first operating in SAR mode allowing a much better height retrieval over the ocean and inland waters. The mission also benefits from the Open-Loop Tracking Command mode, where an a-priory elevation mask improves the performance over inland waters. This study analyses the performance and trends of the OCEAN and OCOG retracker functions in both, Ku and C band over Lake Issyk Kul. We make use of GNSS-derived lake profiles and information from shore-based tide gauges to analyze uninterrupted data series. We found biases of 2 ± 41 mm for Sentinel-3A and −45 ± 37 mm for Sentinel-3B for the OCEAN retracker and 307 ± 29 mm for Sentinel-3A and 345 ± 22 mm for Sentinel-3B using the OCOG retracker. Moreover, our results give evidence to small drifts for both satellites and also for both retracker.

Global sea level shows an increasing trend for several decades driven mainly by climate change. Absolute Sea Level (ASL) changes can only be extracted from Relative Sea Level (RSL) measurements with proper reduction of vertical land movements of the bench marks. Atomic clocks at those tide gauges can potentially provide the absolute, near real-time physical height change. High-performance clocks with an uncertainty of 1 0 −18 $$10^{-18}$$ enable a height measurement with 1 cm accuracy. As RSL is related to regional tidal datums, one has to account for the local variations to obtain a globally consistent measurement of ASL. Hence, by incorporating land motion from clock observations, one can establish a consistent and uniform reference datum for assessing geoid-based absolute sea level changes worldwide.

International reference frames play a pivotal role in metrological applications related to the Earth sciences, covering critical areas such as geodetic reference frames, global change research, deformation processes, and global mass transport. Despite substantial advancements in measurement precision over the past two decades, there are still discrepancies at the centimeter level presenting a persistent challenge. In this paper, we investigate a promising approach to address these subtle error sources, affecting critical parts of the measurement equipment despite the presence of calibration methods.We have built a novel measurement constraint, based on a precise clock and active time delay compensation. By comparing the timing signals in a geodetic measurement system constantly against a precisely controlled optical ruler, we can identify variable system delays that were previously inaccessible. In this way, we introduce a novel tie to the geodetic measurement techniques that can even capture instrumental delay variations over several months.

An assessment of the tropospheric parameters independently derived from the analysis of Very Long Baseline Interferometry (VLBI) and Global Navigation Satellite Systems (GNSS) data serves as a cross-validation of the two space geodetic techniques on the parameter level. Time series of the tropospheric parameters are studied for the most frequently observed VLBI stations at 7 co-located sites covering a time span between 2019 and middle of 2023. These sites are equipped in total with 10 small and fast-slewing antennas that have been specifically built to satisfy the concept of the VLBI Global Observing System (VGOS). Next to the VGOS antennas, 5 legacy VLBI antennas are located providing an additional source of the VLBI observations for comparison. VLBI conducts observations on a session-wise basis of 24 hours at least twice a week, whereas GNSS observes continuously. As a consequence, the paired tropospheric parameters are restricted to epochs where VLBI data are available. The closest GNSS receivers are chosen next the VGOS or VLBI antennas to ensure the same path propagation delays. For the sake of a meaningful comparison, the parameterization of the troposphere is homogenized between the two techniques in favor of the VLBI analysis: the VLBI observations are scheduled to provide even sky-coverage within every hour. After omitting modelled offsets between the reference points of the VLBI and GNSS antennas expected due to the height differences, the obtained tropospheric estimates of two independent techniques show a good agreement level, which lays within their scatter. The remaining tropospheric variations are averaged at the level of 4-6 mm in terms of root mean square differences. A larger scatter of these tropospheric variations is obtained for a few stations at the level between 8–10 mm. These extreme cases can be explained by specific issues at each individual station, i.e. the short paired time series.

In the past three decades, GNSS-based Integrated Water Vapor (IWV) retrieval has been intensively investigated, and its products have been widely used in meteorology like severe weather event monitoring. The physical model for the inversion of IWV from the tropospheric Zenith Total Delay (ZTD) requires meteorological data at the location of the GNSS station, such as the surface pressure and the atmospheric weighted mean temperature. However, real-time acquisition of the meteorological data is a very challenging task for most GNSS stations. While proposed empirical models such as Global Pressure and Temperature 3 (GPT3) can provide the meteorological data based on their historical information, larger estimation distortions are found in specific mid- and high-latitude regions. Moreover, we analyzed the seasonal variations in GPT3 prediction errors. In view of the above-mentioned problems, this study implements an IWV conversion model based on a feedforward Deep artificial Neural Network (DNN) and Long Short-Term Memory Network (LSTM) network, which learns historical data from GNSS stations and allows real-time ZTD to IWV conversion without the need of actual meteorological observation but of values only GPT3. Results at four selected mid- and high-latitude GNSS stations show that the Root Mean Square Error (RMSE) of the proposed deep learning method decreases from an average of 3.97 mm to 2.84 mm compared to GNSS IWV retrieved from GPT3. The proposed model provides a broad applicability in real-time GNSS IWV prediction without the availability of real-time measured meteorological data.

Improving our understanding of non-tidal loading (NTL) in geodetic time series, especially at regional and local scales, holds paramount importance. This deeper comprehension enables accurate modeling and effective removal of NTL effects from the time series, consequently enhancing the overall stability and reliability of geodetic observations. In this study, we compared the performance of different loading products and investigated their impact on the 20-year time series of four permanent GNSS stations within the Finnish permanent GNSS network (FinnRef). We employed original GNSS time series data products generated by four different analysing centers. We qualitatively compared NTL corrections involving ten different combinations of different hydrological, non-tidal atmospheric, and non-tidal oceanic loading models to see how various loading configurations operate and how they affect the noise characteristics of GNSS 3D time series, and ultimately to figure out which models are the most realistic in Finland. We observed weighted RMS reduction rates of up to 20% for the vertical coordinate and up to 10% for the horizontal coordinate. Additionally, we identified a maximum annual amplitude reduction rate of 87.2%. The results demonstrate a substantial improvement through the integration of hydrological loading products derived from GRACE satellites in our study conducted over Finland.

Geostrophic currents, driven by the Coriolis and pressure gradient forces, are crucial for understanding ocean circulation. The Antarctic Circumpolar Current (ACC) in the Southern Ocean, which surrounds Antarctica, has a significant global impact, and its volume transport (VT) remains a challenge to measure. We use satellite data, combining altimetry and gravity satellite missions, to estimate VT within the ACC region. Our study provides a comprehensive spatial and temporal analysis, including both barotropic and baroclinic VT components. The spatial analysis reveals a mean VT of 210.44 ± 3.4 Sv for the entire study area, with maxima near critical choke points. Focusing on the time-varying component, we identify a mean VT of 15.86 ± 0.05 Sv per 1° grid cell, a linear trend of −0.007 ± 0.002 Sv per month, and significant seasonal and biannual signals. The baroclinic component drives low-frequency variability, while the barotropic component controls high-frequency variability. We propose a specific ACC zonal VT of 201.63 ± 0.71 Sv. We validate our results with in situ measurements from the Drake Passage. In conclusion, our satellite-based approach provides valuable insights into the ACC VT. This methodological extension improves our understanding of the ocean circulation dynamics of the ACC and demonstrates the utility and robustness of satellite data in oceanographic research.

Throughout the earthquake cycling at fault zones, Earth’s crust undergoes deformations. GNSS coordinate time series record linear tectonic motion, seismic displacements, postseismic decays, and periodic signatures such as non-tidal loading. Any additional motions can be classed as transient tectonic signals, i.e., unexpected accelerations with respect to the standard trajectory model. As the number of permanent stations increases and as time series grow, we are increasingly able to recognise transient tectonic signals. Since some of these suspected tectonic transients have subtle magnitudes or sometimes unusual spatiotemporal features, we need to develop methods for determining which transients are artifacts and which are of tectonic origin.Here, we investigate the impact of certain GNSS processing choices and how they affect the appearance of transients in the GNSS displacement time series solutions. In this study, we choose data from Cascadia, a region for which the occurrence of transient signals in the GNSS time series is well known. We processed data based from 189 selected stations in network mode for the time span 2015 to 2019. After producing coordinate time series, we then built a pipeline to isolate processing artifacts and tectonic transients, using the regression model-based algorithm known as GrAtSiD (Greedy Automatic Signal Decomposition).The residuals of GNSS observations show that most sites have a precision of 5 mm to 10 mm. Using the GrAtSiD algorithm, we detected transient signals with velocities exceeding 0.3 mm/day near the ALBH station.

Without geodesy – the science that determines the shape of the Earth, its gravity field, and its rotation as functions of space and time – accurate positioning would not be possible. Geodetic observation techniques, analysis infrastructure, and products provided by the International Association of Geodesy (IAG) are fundamental to Earth system research and are the backbone for location-based applications. IAG’s Global Geodetic Observing System (GGOS) is a collaborative effort of the global geodesy community aimed at providing consistent and openly accessible geodetic Earth observations. In addition, GGOS supports activities and projects that promote the importance of geodesy to science and society. This paper summarizes recent GGOS initiatives and achievements in strengthening the awareness of the value of geodesy.

The European Plate Observing System (EPOS) is a large and complex European e-infrastructure that facilitates the integrated use of multi-disciplinary datasets and services for Solid Earth research. EPOS’ GNSS (Global Navigation Satellite Systems) component provides access to GNSS data and products. This paper introduces a new EPOS web portal ( https://gnssquality-epos.oma.be ) that has been developed with the aim to provide the necessary information to monitor the availability and quality of daily GNSS data that are discoverable through EPOS. Currently, the web portal includes the tracking performances of more than 1600 GNSS stations. Several GNSS data quality indicators (DQIs), such as the number of observed versus expected observations, the number of missing epochs, the number of observed satellites, the maximum number of observations, the number of cycle slips, the Standard Point Positioning results, and the multipath values on code observation are monitored and their plots are available online. These DQIs provide helpful information that can be used to detect a potential degradation of the quality of the GNSS observations. Here, we will present the status of the web portal, the considered data quality indicators, and their benefits for GNSS data users.

Monitoring the Earth is undertaken in numerous geometric and physical reference frames and coordinate reference systems. Analysis often requires transformation of coordinates between these frames. As the accuracy of positioning and geospatial data improves, the use of gridded data to describe the quantities used in these coordinate transformations is increasing. Rectangular grids also provide an efficient means of disseminating other geodetic data. IAG Commission 1 Working Group 1.3.1 in association with the Open Geospatial Consortium (OGC) have developed a Geodetic data Grid eXchange Format (GGXF) for quantifying and disseminating gridded geodetic data. GGXF was developed in conjunction with a functional model for crustal deformation (FMCD) including support for time-dependent changes, but has been designed to support any type of regularly-gridded geodetic data including but not limited to geoid models, offsets between reference frames (of one, two or three dimensions), velocity grids, tidal surfaces, etc. The purpose of GGXF is to provide a single comprehensive, efficient distribution format through which producers can disseminate gridded geodetic data and users can exchange and apply this information. This paper presents an overview of the GGXF format.

Time series of interferometric SAR (InSAR) images offer the potential to detect and monitor surface deformation with high spatial resolution, even for slow deformation processes. However, many different sources contribute to phase changes which are used in InSAR to estimate displacements. Complex displacement mechanisms or strong atmospheric contributions can complicate the separation of these contributions and even cause problems when unwrapping the phase. A preliminary model of expected displacements can support this process but requires information about all involved deformation processes. However, as these processes are often the main subject of the investigation, they are not sufficiently understood in advance.In this contribution, we approach this issue by analyzing InSAR time series results of regions with complex deformation behavior with the established statistical methods of principal and independent component analysis to identify dominant displacement patterns. We study Sentinel-1 InSAR data from 2015 to 2022 above the storage cavern field Epe in North Rhine Westphalia, Germany. Epe displays a spatially and temporally complex surface deformation field, which was described in previous studies as consisting of a linear signal relating to the cavern convergence as well as of seasonal and cavern pressure-dependent contributions. Our resulting displacement components can be clearly separated and appointed to different sources. This is supported by ground truth data and supplemental measurements of cavern pressure levels and groundwater levels. We also find that the previously described linear parametrization of displacements related to cavern convergence is no longer sufficient for longer time series.Our results show that we can obtain source-dependent displacement models from long and complex InSAR time series when using ICA. These can then either be used to refine time series processing or to describe the physical processes causing to the surface displacements with a geophysical source model. Both will be the subject of future investigations.